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Heavy Quarkonium States with the Holographic Potential Defu Hou (CCNU) With Hai-cang Ren,JHEP 0801:029,2008. 0710.2639 From Strings to Things , Seattle , May 2008
OUTLINES • Introduction • Holographic potential model from AdS/CFT • Holographic potential model with IR cut. • Concluding remarks
Introduction Many interesting phenomena in QCD lie in the strongly-coupled region. Non-perturbative methods for analysis Lattice: problematic with finite chemical potentioal, time- dependent problems AdS/CFT: Notable success in RHIC physics Viscosity, Jet quenching, …
Heavy meson melting • At T<Tc, confined ,potenial linearing rises • At T>Tc, deconf. Short range attraction range: screening length Lsc As T↗, Lsc↘, there exists a Td : the potential no longer binding for T>Td ( Melting Temperature) Heavy quakonium melting is an important signal of QGP
Nonperturbative calculation of Td • Potential model Lattice F. Karsch , Brambilla… AdS/CFT Maldacena, Rey, Liu , Avramis • Spectral function Lattice Karch AdS/CFTHoyos, Kim et al
Extracting V(r) from Wilson loop t 1/T r Q Q
F(r,t) is the free energy excess of a static pair of qq The internal energy reads
F-ansatz V(r) =F(r,T) • U –ansatz V(r)=U(r, T)
Poential From Lattice • Quarkonium probes non-perturbative information about medium. How? Matsui, Satz 1986 • Wilson loop is static time-like and in fundamental representation: • Wilson loop is calculable in lattice QCD time Bielefeld Group, hep-lat/0509001 Ltime L distance
= Field TheoryGravity Theory Gauge Theories QCD Quantum Gravity String theory Holography the large N limit Supersymmetric Yang Mills N large Gravitational theory in 10 dimensions Calculations Correlation functions Quark-antiquark potential
Potential from AdS/CFT • According to the holographic principle, the thermal average of a Wilson loop operator in 4D N=4 SUSY YM at large N_c and large 't Hooft coupling corresponds to the minimum area of the string world sheet in the 5D AdS metric with a Euclidean signature,
q q q r r q y _ + BH
Numerical Results • Value of ‘t Hooft coupling. • Upper limit : QCD value of coupling at RHIC • Lower limit: heavy quark potential , (Gubser) • Mc=1.65Gev, Mb=4.85Gev, Tc=186MeV
Dissociate Temperature Td in MeV
Holographic potential model with an IR cutoff Hard Wall : Erlich, Katz, Son, Stephanov
In the hadronic phase • In the plasma phase
Soft-wall model 1 : Karch, Katz, Son, Stephanov A dilaton is introduced, Metrics are the same. • Soft-wall model 2 : Andreev,Zakharov;Kajantie modify string frame metric by a conformal factor
Summary We calculated dissociation temperatures Td of heavy quarkonium states from holographic potential The computed Td have remarkable features compariable with that from Lattice To assess the validity . At melting temperature of U satz